Irreducible quasi-D-overlap functions: Matrix representation and diagonal generation

As an emerging mathematical model of information aggregation successfully applied in image processing, pattern recognition, decision-making and etc, theoretical research of overlap functions has also continued to develop, especially the research on their related derivative concepts that have emerged in recent years. This work considers so-called irreducible quasi-D-overlap functions defined on grid of unit square, which are one class of discrete aggregation operators originated from overlap functions. The core contents are: (i) it presents the concept of irreducible quasi-D-overlap functions and shows basic properties of them; (ii) it provides equivalent characterization of irreducible quasi-D-overlap functions by means of strong permutation matrixes; (iii) it gives a construction manner for irreducible quasi-D-overlap functions by means of so-called diagonal operators and the greatest and smallest irreducible quasi-D-overlap functions with given diagonal operator are obtained. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper presents the theoretical research of overlap functions and their related derivative concepts, focusing on the concept, properties, and construction methods of irreducible quasi-D-overlap functions defined on a grid of unit square.